A lot of the punish game is learning combo trees and which moves to use for what purposes. Ivysaur isn't a great example for this given how difficult she is to combo in general, but you certainly need to get C4s on your opponents, and that's usually easiest at lower percents off of u-throw. The forum does offer a lot of resources for comprehending the various combo trees, and it's easiest to break them up into a floaty / fast-faller spectrum and understanding where each character lies on that spectrum: Ivysaur is far to the floaty end and thus doesn't have a ton of combo potential outside of low-knockback moves like down air, nair, cypher, and f-tilt. The benefit there is that they die extremely early to upward KO moves (which are most of Snake's KO options). Fast fallers meanwhile get wrecked but u-throw, u-tilt, and all the other launching moves Snake has. For example, the basic combo I go for on Fox at 0% is to u-throw into jab (they usually try to tech and end up sitting in shield instead since jab doesn't cause tumble, meaning they can't tech it) allowing me to regrab, then I'll u-throw again into u-tilt (which starts to be an option at ~25%), which leads into a guaranteed regrab into a chain grab that gets them up to 80% easily. At that point, all I need is a C4 (easy enough to get off of the throw) and one more win in the neutral game (read as: one more punish opportunity) to launch them into a KO via C4. Sometimes you can even get a C4 into techchase regrab immediately into u-throw -> u-air -> C4, or you can sneak in a nair or d-air to work the same way as the jab at the start of the combo to prevent their tech and mix up their reaction. This same string works on Falcon, Falco, Wolf, Roy, and Zero Suit Samus to varying degrees as well. It's all character specific, but I believe Snake has the tools to really mess up any character enough for C4 to KO them.
Edgeguarding is really important against Ivysaur, though, considering her recovery is pretty bad overall. The main boon that Ivysaur has is that she can throw out really quick, safe hitboxes to challenge ledgehoggers, so you've got to scope all of that out beforehand. The reason that's important is that Ivysaur's UpB only has two uses and Ivysaur's only other recovery option is a single down air stall and air dodge. If you're also occupying ledge while Ivysaur is trying to Up B tether, the Ivysaur is stuck doing a super laggy getup animation (granted they still have the option of fading forward or fading back). The big deal here is two-fold:
- If they fade forward, they land on stage with substantial landing lag, meaning you can get a free C4 OR a free tranq, assuming you already have the C4 or have the time to both stick and launch the Ivysaur—depends slightly on their mashing but also on their percentage.
- Alternatively, if they're at KO percent and/or have a C4 on them, you can also place a mine to cover the most inward fade, as the most outward fade forces them to regrab ledge (which they can't do if you ledgehog them). This puts them in a horrible position given that you can freely force them into the mine, which means you can force the KO.
This is "covering the options" as BND said, and I do have to disclaim that I am simplifying the scenario greatly, and Ivysaur surely is a lot more versatile than just that, but other characters like Sheik and Falcon and easily die off of a single back throw off stage simply due to Snake's great edgeguarding capabilities. Spacies additionally get ruined by an unexpected back throw since you can quickly wavedash to ledge into invincible ledgehop/drop back air to catch their side-b or up B. Cypher also beats out their side-b's and links into back air, which is a really flashy but completely guaranteed edgeguard if you get the read on it. Add in the opportunity to C4 them into a forward air or back air and edgeguarding spacies becomes little more than pushing them until they're just too far to return. I'm sure there's also something to be said of utilizing C4 on the ledge to stuff sweetspot attempts (possibly using your shield to extend the hitbox duration via hitlag). Something like C4 drop into shield pivot FH back air OOS is in my brain right now.
tl;dr version: this character is hard. You need to study a lot if you want to succeed with him without having a genuinely concrete understanding of the game as a whole (i.e. great fundamentals leading to a superior neutral game à la Professor Pro or Messi).
The benefit right now is that many people (Prof, Messi, Myself, BND, Rolex, etc.) provide the resources to accelerate the process somewhat, either through videos or data collection or experimentation. Keep an eye on what everyone here is doing and you'll do well, I think. Ask questions about any specific thing that confuses or intrigues you during your research, and be sure to pursue it to the fullest as well. I'm just now finding out the benefits of u-air and back air's weak hitboxes as methods of extending combos, and it's taking me forever to acclimate to proper follow-ups out of Cypher, just to name a few examples.
